This invention relates to an exposure mask and a method of producing a mask pattern used for calibration in formation of a mask pattern to be used for exposure to form a three-dimensional shape of an optical lens array or a like device.
Various methods of producing very small optical parts such as a microlens array used in applied products of image devices such as a CCD (Charge Coupled Device) or LCD (Liquid Crystal Display) unit are available, and one of such methods applies a photolithography technique used in manufacture of semiconductor and liquid crystal devices.
In the method just mentioned, a desired exposure amount distribution is applied to photo-resist which is a photosensitive material, and the photo-resist is developed so that it is worked three-dimensionally. Then, the worked photo-resist is used as a mask to perform etching to three-dimensionally work a silicon, glass or like substrate.
The photo mask used in the lithography process is implemented by such multiple exposure using a plurality of masks as seen in FIG. 14. The exposure method according to this technique is described in connection with one-dimensional exposure. The final exposure light distribution is represented by D(X) in FIG. 14.
First, light of an exposure light amount E[1] is applied to a region <1> using a mask (1) in FIG. 14. Then, light of another exposure light amount E[2] is applied to another region <2> including the region <1> using another mask (2). At this time, the total exposure light amount D1 to the region <1> is E[1]+E[2]. Further, exposure is successively performed with exposure amounts E[3], E[4],  . . . , E[n] using further masks (3), (4), . . . (not shown) and (n), respectively. Consequently, the final exposure light amount D[i] to the region i is given by D[i]=E[i]+E[i+1]+ . . . +E[n], and a desired discrete exposure light amount distribution is obtained. In this instance, the number n of masks corresponds to the exposure light amount position resolution, and for example, where n=10, 10 exposure light amount steps are obtained.
Recently, in addition to the multiple exposure method which uses a plurality of masks, another method has been developed wherein a desired exposure light amount distribution is obtained by a single exposure operation using a so-called gray tone mask wherein the transmission factor of a light intercepting film has a continuous distribution as disclosed in Japanese Patent Laid-Open No. 2002-189280 (hereinafter referred to as Patent Document 1). A concept of the gray tone mask is illustrated in FIG. 15.
Of the two methods described above, the former method which utilizes a plurality of masks involves multiple exposure by a plurality of exposure operations multi-stage exposure also in time, and therefore, a resulting integrated exposure light amount distribution includes a remaining stepwise configuration. Further, the number of obtainable exposure light amount gradations is equal to the number of masks and hence to the number of times of exposure operations, and there is a problem that practically the number is approximately ten and a sufficient number of gradations cannot be obtained. Further, the exposure process is complicated and a mask cost which increases in proportion to the number of masks is required, and they give rise to various problems.
On the other hand, the latter method which involves a single exposure operation by a gray tone mask as disclosed in Patent Document 1 is advantageous in that a substantially continuous exposure light amount distribution is obtained. However, generally it is very difficult to produce such a gray tone mask as described above and a special film material and a special mask formation processing technique are required, resulting in a very high mask cost. Further, the special film material provides a matter of concern in regard to a secular change by heat and further provides a matter of concern in regard to the problem of the stability in performance during its use (that is, the stability against heat caused by absorption of light for exposure).
As a countermeasure for the problems described above, the assignee of the present patent application has proposed a method wherein a mask is formed with binary mask patterns of a pitch smaller than a resolution limit pitch and the opening size or dot remaining pattern size is spatially varied to allow formation of an arbitrary three-dimensional structure.
FIG. 16 illustrates a concept of a mask pattern for forming a one-dimensional concave lens array from positive resist in accordance with the method just described. Upon designing such a mask as seen in FIG. 16, the following designing procedure is taken. In particular, the intensity of 0th order light of a single two-dimensional array pattern of a certain pitch (which is smaller than a resolution limit pitch determined from NA, σ and λ as represented by an expression (1) given below) and a certain opening size is theoretically calculated, and an opening size for obtaining a predetermined light amount at a predetermined position is derived based on the calculated strength of 0th order light. Then, the opening size is changed depending upon the place so that a desired thickness of the remaining resist film may be obtained at a predetermined position.Pmin=λ/{NA×(1+σ)}  (1)
Masks were actually produced as prototypes and photo-resist was formed in a predetermined three-dimensional structure (lens array or the like) on the masks based on the design procedure described above. The three-dimensional structure has some error in formation height as seen, for example, in FIG. 17 or 18.
It can be seen that, as a tendency of the error, the error is great in the formation height at a place at which the opening size is small, that is, at a place at which the mask transmission factor is low. It is considered that, as possible causes, the tendency of the error is caused by (1) an error of the opening size itself (mask production error) and (2) a generation of “fogging exposure” by flare in an exposure apparatus where a great amount of exposure light is provided, resulting in a generation of an exposure light amount like a DC component in all over area of the exposure field.
In particular, FIG. 17 schematically shows the error in the case of (1) above. Referring to FIG. 17, an error arising from the manufacture is produced on a light intercepting pattern size of a mask pattern and has an influence on the exposure light amount to cause an error in the height of the lens.
Meanwhile, FIG. 18 schematically shows the error in the case of (2) above. Referring to FIG. 18, also where it is assumed that a mask pattern has no error (mask error) arising from the manufacture, since the fogging exposure light amount by flare of the exposure apparatus is involved by several percent, the fogging exposure light amount is added to cause an error in the height of the lens to be formed. It is to be noted that, in FIGS. 17 and 18, the solid lines represent design values and the broken lines represent errors.
In addition to the errors described above, the characteristics of the exposure light amount and the remaining resist film height exhibit some difference between designed ones and actual ones because the correlation between the development rates at the surface layer portion and the internal portion of the resist film is somewhat different depending upon whether a three-dimensional structure does not exist (upon designing) or exists (in actual production) in the resist layer at the development step. Consequently, the controllability of the resist remaining film height after the development in the proximity of the resist surface layer is deteriorated.
Therefore, a problem occurs that, if a portion of the resist near the surface is left to form a shape, then an error appears between the height of the remaining film of the resist formed with the set exposure light amount and the height of the actual remaining film and therefore the desired shape cannot be obtained.
Meanwhile, a theoretical model of a development process in which a three-dimensional structure is formed in this manner has not been clarified as yet, and it is difficult to accurately predict a remaining film distribution of resist by a simulation or the like.